TY - GEN

T1 - Typical peak sidelobe level of binary sequences

AU - Litsyn, Simon

AU - Shpunt, Alexander

PY - 2008

Y1 - 2008

N2 - For a binary sequence Sn = {si}n i=1 ∈{±1}n, the peak sidelobe level (PSL) is defined as M(Sn) = max k=1,2,...., n-1 | ∑ i=1 n-k SiSi+k|. It is shown that the distribution of M(Sn) is strongly concentrated, and asymptotically almost surely, γ(Sn) = M(Sn)/√ n ln n ∈ [1, √ 2]. Explicit bounds for the number of sequences outside this range are provided. This improves on the best earlier known bounds due to Moon and Moser [8] claiming that the typical value γ(Sn) ∈ [o (1/√ ln n), 2], and settles to the affirmative a conjecture of Dmitriev and Jedwab [2] on the growth rate of the typical peak sidelobe.

AB - For a binary sequence Sn = {si}n i=1 ∈{±1}n, the peak sidelobe level (PSL) is defined as M(Sn) = max k=1,2,...., n-1 | ∑ i=1 n-k SiSi+k|. It is shown that the distribution of M(Sn) is strongly concentrated, and asymptotically almost surely, γ(Sn) = M(Sn)/√ n ln n ∈ [1, √ 2]. Explicit bounds for the number of sequences outside this range are provided. This improves on the best earlier known bounds due to Moon and Moser [8] claiming that the typical value γ(Sn) ∈ [o (1/√ ln n), 2], and settles to the affirmative a conjecture of Dmitriev and Jedwab [2] on the growth rate of the typical peak sidelobe.

UR - http://www.scopus.com/inward/record.url?scp=52349089358&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2008.4595289

DO - 10.1109/ISIT.2008.4595289

M3 - פרסום בספר כנס

AN - SCOPUS:52349089358

SN - 9781424422579

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 1755

EP - 1757

BT - Proceedings - 2008 IEEE International Symposium on Information Theory, ISIT 2008

Y2 - 6 July 2008 through 11 July 2008

ER -